According to the soundness lemma in [1]}, if the properties \(1-3\)  in Theorem 1 hold for consensus rounds \(\lbrace 0,1,\cdots ,r-1\rbrace \) , then properties 1 and 3 hold for consensus round \(r\) , when the consensus leader \(n_{l^{r}}\)  is malicious. In the case of \(n_{l^{r}}\)  being malicious, its proposal will be replaced by an honest users' proposal if it satisfies the condition defined in Lemma REF  as evaluated by the honest users. Even if that is not the case, the consensus process will happen according to the original methodology. Therefore, the soundness of the network will remain intact even with the proposed modifications.
